You only have to look through any page of the GRO index for the 1920s and see how many children have been registered in a surname with the exact same surname showing for the mother's maiden name. It was a time when women were able to work at more skilled trades due to the lack of man power post war and they had a new type of independence. I find it quite often and of course it is disapointing that it means the loss of a line to persue. Sometimes there would be an entry in a baptism register naming a father, but not very often and not as late as the 1920s probably. It is possible that at their marriage, a child without a named father on their birth certificate may name a father on their marriage certificate, as to marry as illegitimate even into the 1950s and 60s was scandalous and of course more public than a private birth registration.